scholarly journals The Kell Calculus: Operational Semantics and Type System

2003 ◽  
pp. 109-123 ◽  
Author(s):  
Philippe Bidinger ◽  
Jean-Bernard Stefani
Keyword(s):  
Operational Semantics ◽  
Type System

FIRST-CLASS CONTEXTS IN ML

2000 ◽  
Vol 11 (01) ◽  
pp. 65-87
Author(s):  
MASATOMO HASHIMOTO
Keyword(s):  
Programming Language ◽  
Operational Semantics ◽  
Type System ◽  
Type Inference ◽  
Inference Algorithm ◽  
Hole Filling ◽  
Dynamic Binding ◽  
Polymorphic Type ◽  
Open Program ◽  
Program Modules

This paper develops an ML-style programming language with first-class contexts i.e. expressions with holes. The crucial operation for contexts is hole-filling. Filling a hole with an expression has the effect of dynamic binding or macro expansion which provides the advanced feature of manipulating open program fragments. Such mechanisms are useful in many systems including distributed/mobile programming and program modules. If we can treat a context as a first-class citizen in a programming language, then we can manipulate open program fragments in a flexible and seamless manner. A possibility of such a programming language was shown by the theory of simply typed context calculus developed by Hashimoto and Ohori. This paper extends the simply typed system of the context calculus to an ML-style polymorphic type system, and gives an operational semantics and a sound and complete type inference algorithm.

scholarly journals Object Cloning for Ownership Systems

2021 ◽  
Author(s):  
◽  
Paley Guangping Li
Keyword(s):  
Comparative Analysis ◽  
Programming Languages ◽  
Formal Model ◽  
Operational Semantics ◽  
Type System ◽  
Object Oriented ◽  
Object Oriented Programming ◽  
Constraint System ◽  
Existential Quantification ◽  
Ownership Types

<p>Modern object-oriented programming languages frequently need the ability to clone, duplicate, and copy objects. The usual approaches taken by languages are rudimentary, primarily because these approaches operate with little understanding of the object being cloned. Deep cloning naively copies every object that has a reachable reference path from the object being cloned, even if the objects being copied have no innate relationship with that object. For more sophisticated cloning operations, languages usually only provide the capacity for programmers to define their own cloning operations for specific objects, and with no help from the type system.  Sheep cloning is an automated operation that clones objects by leveraging information about those objects’ structures, which the programmer imparts into their programs with ownership types. Ownership types are a language mechanism that defines an owner for every object in the program. Ownership types create a hierarchical structure for the heap.  In this thesis, we construct an extensible formal model for an object-oriented language with ownership types (Core), and use it to explore different formalisms of sheep cloning. We formalise three distinct operational semantics of sheep cloning, and for each approach we include proofs or proof outlines where appropriate, and provide a comparative analysis of each model’s benefits. Our main contribution is the descripSC formal model of sheep cloning and its proof of type soundness.  The second contribution of this thesis is the formalism of Mojo-jojo, a multiple ownership system that includes existential quantification over types and context parameters, along with a constraint system for context parameters. We prove type soundness for Mojo-jojo. Multiple ownership is a mechanism which allows objects to have more than one owner. Context parameters in Mojo-jojo can use binary operators such as: intersection, union, and disjointness.</p>

Typing and subtyping for mobile processes

1996 ◽  
Vol 6 (5) ◽  
pp. 409-453 ◽  
Author(s):  
Benjamin Pierce ◽  
Davide Sangiorgi
Keyword(s):  
Process Algebra ◽  
Operational Semantics ◽  
Type System ◽  
Higher Order ◽  
Order Process ◽  
Process Calculi ◽  
Mobile Processes

The π-calculus is a process algebra that supports mobility by focusing on the communication of channels. Milner's presentation of the π-calculus includes a type system assigning arities to channels and enforcing a corresponding discipline in their use. We extend Milner's language of types by distinguishing between the ability to read from a channel, the ability to write to a channel, and the ability both to read and to write. This refinement gives rise to a natural subtype relation similar to those studied in typed λ-calculi. The greater precision of our type discipline yields stronger versions of standard theorems on the π-calculus. These can be used, for example, to obtain the validity of β-reduction for the more efficient of Milner's encodings of the call-by-value λ-calculus, which fails in the ordinary π-calculus. We define the syntax, typing, subtyping, and operational semantics of our calculus, prove that the typing rules are sound, apply the system to Milner's λ-calculus encodings, and sketch extensions to higher-order process calculi and polymorphic typing.

scholarly journals Shifting the stage

2011 ◽  
Vol 21 (6) ◽  
pp. 617-662 ◽  
Author(s):  
YUKIYOSHI KAMEYAMA ◽  
OLEG KISELYOV ◽  
CHUNG-CHIEH SHAN
Keyword(s):  
Gaussian Elimination ◽  
Operational Semantics ◽  
Type System ◽  
Static Properties ◽  
Code Generator ◽  
Domain Experts ◽  
Wrong Side ◽  
Code Generators ◽  
Early Error ◽  
Efficient Code

AbstractIt is often hard to write programs that are efficient yet reusable. For example, an efficient implementation of Gaussian elimination should be specialized to the structure and known static properties of the input matrix. The most profitable optimizations, such as choosing the best pivoting or memoization, cannot be expected of even an advanced compiler because they are specific to the domain, but expressing these optimizations directly makes for ungainly source code. Instead, a promising and popular way to reconcile efficiency with reusability is for a domain expert to write code generators.Two pillars of this approach are types and effects. Typed multilevel languages such as MetaOCaml ensure safety and early error reporting: a well-typed code generator neither goes wrong nor generates code that goes wrong. Side effects such as state and control ease correctness and expressivity: An effectful generator can resemble the textbook presentation of an algorithm, as is familiar to domain experts, yet insert let for memoization and if for bounds checking, as is necessary for efficiency. Together, types and effects enable structuring code generators as compositions of modules with well-defined interfaces, and hence scaling to large programs. However, blindly adding effects renders multilevel types unsound.We introduce the first multilevel calculus with control effects and a sound type system. We give small-step operational semantics as well as a one-pass continuation-passing-style translation. For soundness, our calculus restricts the code generator's effects to the scope of generated binders. Even with this restriction, we can finally write efficient code generators for dynamic programming and numerical methods in direct style, like in algorithm textbooks, rather than in continuation-passing or monadic style.

Parallel functional programming on recursively defined data via data-parallel recursion

1999 ◽  
Vol 9 (4) ◽  
pp. 427-462 ◽  
Author(s):  
SUSUMU NISHIMURA ◽  
ATSUSHI OHORI
Keyword(s):  
Parallel Processing ◽  
Functional Programming ◽  
Formal Semantics ◽  
Operational Semantics ◽  
Type System ◽  
Parallel Execution ◽  
System Of Equations ◽  
Functional Language ◽  
Data Parallel ◽  
Evaluation Mechanism

This article proposes a new language mechanism for data-parallel processing of dynamically allocated recursively defined data. Different from the conventional array-based data- parallelism, it allows parallel processing of general recursively defined data such as lists or trees in a functional way. This is achieved by representing a recursively defined datum as a system of equations, and defining new language constructs for parallel transformation of a system of equations. By integrating them with a higher-order functional language, we obtain a functional programming language suitable for describing data-parallel algorithms on recursively defined data in a declarative way. The language has an ML style polymorphic type system and a type sound operational semantics that uniformly integrates the parallel evaluation mechanism with the semantics of a typed functional language. We also show the intended parallel execution model behind the formal semantics, assuming an idealized distributed memory multicomputer.

scholarly journals Contextual modal types for algebraic effects and handlers

2021 ◽  
Vol 5 (ICFP) ◽  
pp. 1-29
Author(s):  
Nikita Zyuzin ◽  
Aleksandar Nanevski
Keyword(s):  
Programming Languages ◽  
Type Theory ◽  
Operational Semantics ◽  
Algebraic Theory ◽  
Type System ◽  
Effect Theory ◽  
Explicit Substitutions ◽  
Type And Effect Systems ◽  
Modal Type ◽  
Modal Types

Programming languages with algebraic effects often track the computations’ effects using type-and-effect systems. In this paper, we propose to view an algebraic effect theory of a computation as a variable context; consequently, we propose to track algebraic effects of a computation with contextual modal types . We develop ECMTT, a novel calculus which tracks algebraic effects by a contextualized variant of the modal □ (necessity) operator, that it inherits from Contextual Modal Type Theory (CMTT). Whereas type-and-effect systems add effect annotations on top of a prior programming language, the effect annotations in ECMTT are inherent to the language, as they are managed by programming constructs corresponding to the logical introduction and elimination forms for the □ modality. Thus, the type-and-effect system of ECMTT is actually just a type system. Our design obtains the properties of local soundness and completeness, and determines the operational semantics solely by β-reduction, as customary in other logic-based calculi. In this view, effect handlers arise naturally as a witness that one context (i.e., algebraic theory) can be reached from another, generalizing explicit substitutions from CMTT. To the best of our knowledge, ECMTT is the first system to relate algebraic effects to modal types. We also see it as a step towards providing a correspondence in the style of Curry and Howard that may transfer a number of results from the fields of modal logic and modal type theory to that of algebraic effects.

Types and typechecking for Communicating Quantum Processes

2006 ◽  
Vol 16 (3) ◽  
pp. 375-406 ◽  
Author(s):  
SIMON J. GAY ◽  
RAJAGOPAL NAGARAJAN
Keyword(s):  
Communication Systems ◽  
Quantum Communication ◽  
Formal Analysis ◽  
Operational Semantics ◽  
Type System ◽  
Quantum Processes ◽  
Classical Communication ◽  
Quantum Bits ◽  
Classical Systems ◽  
Pi Calculus

We define a language CQP (Communicating Quantum Processes) for modelling systems that combine quantum and classical communication and computation. CQP combines the communication primitives of the pi-calculus with primitives for measurement and transformation of the quantum state; in particular, quantum bits (qubits) can be transmitted from process to process along communication channels. CQP has a static type system, which classifies channels, distinguishes between quantum and classical data, and controls the use of quantum states. We formally define the syntax, operational semantics and type system of CQP, prove that the semantics preserves typing, and prove that typing guarantees that each qubit is owned by a unique process within a system. We also define a typechecking algorithm and prove that it is sound and complete with respect to the type system. We illustrate CQP by defining models of several quantum communication systems, and outline our plans for using CQP as the foundation for formal analysis and verification of combined quantum and classical systems.

scholarly journals Typing first-class continuations in ML

1993 ◽  
Vol 3 (4) ◽  
pp. 465-484 ◽  
Author(s):  
Robert Harper ◽  
Bruce F. Duba ◽  
David Macqueen
Keyword(s):  
Operational Semantics ◽  
Type System ◽  
Type Systems ◽  
Functional Language ◽  
Type Assignment ◽  
Polymorphic Type ◽  
Alternative Type

AbstractAn extension of ML with continuation primitives similar to those found in Scheme is considered. A number of alternative type systems are discussed, and several programming examples are given. A continuation-based operational semantics is defined for a small, purely functional language, and the soundness of the Damas–Milner polymorphic type assignment system with respect to this semantics is proved. The full Damas–Milner type system is shown to be unsound in the presence of first-class continuations. Restrictions on polymorphism similar to those introduced in connection with reference types are shown to suffice for soundness.

scholarly journals Object Cloning for Ownership Systems

2021 ◽  
Author(s):  
◽  
Paley Guangping Li
Keyword(s):  
Comparative Analysis ◽  
Programming Languages ◽  
Formal Model ◽  
Operational Semantics ◽  
Type System ◽  
Object Oriented ◽  
Object Oriented Programming ◽  
Constraint System ◽  
Existential Quantification ◽  
Ownership Types

<p>Modern object-oriented programming languages frequently need the ability to clone, duplicate, and copy objects. The usual approaches taken by languages are rudimentary, primarily because these approaches operate with little understanding of the object being cloned. Deep cloning naively copies every object that has a reachable reference path from the object being cloned, even if the objects being copied have no innate relationship with that object. For more sophisticated cloning operations, languages usually only provide the capacity for programmers to define their own cloning operations for specific objects, and with no help from the type system.  Sheep cloning is an automated operation that clones objects by leveraging information about those objects’ structures, which the programmer imparts into their programs with ownership types. Ownership types are a language mechanism that defines an owner for every object in the program. Ownership types create a hierarchical structure for the heap.  In this thesis, we construct an extensible formal model for an object-oriented language with ownership types (Core), and use it to explore different formalisms of sheep cloning. We formalise three distinct operational semantics of sheep cloning, and for each approach we include proofs or proof outlines where appropriate, and provide a comparative analysis of each model’s benefits. Our main contribution is the descripSC formal model of sheep cloning and its proof of type soundness.  The second contribution of this thesis is the formalism of Mojo-jojo, a multiple ownership system that includes existential quantification over types and context parameters, along with a constraint system for context parameters. We prove type soundness for Mojo-jojo. Multiple ownership is a mechanism which allows objects to have more than one owner. Context parameters in Mojo-jojo can use binary operators such as: intersection, union, and disjointness.</p>

scholarly journals Annotated Type Systems for Program Analysis

1995 ◽  
Vol 24 (498) ◽  
Author(s):  
Kirsten Lackner Solberg
Keyword(s):  
Program Analysis ◽  
Abstract Interpretation ◽  
Operational Semantics ◽  
Type System ◽  
Denotational Semantics ◽  
Type Systems ◽  
Strictness Analysis ◽  
Binding Time ◽  
The One ◽  
Treat All

<p>In this Ph.D. thesis, we study four program analyses. Three of them are specified by annotated type systems and the last one by abstract interpretation.</p><p>We present a combined strictness and totality analysis. We are specifying the analysis as an annotated type system. The type system allows conjunctions of annotated types, but only at the top-level. The analysis is somewhat more powerful than the strictness analysis by Kuo and Mishra due to the conjunctions and in that we also consider totality. The analysis is shown sound with respect to a natural-style operational semantics. The analysis is not immediately extendable to full conjunction.</p><p>The second analysis is also a combined strictness and totality analysis, however with ``full´´ conjunction. Soundness of the analysis is shown with respect to a denotational semantics. The analysis is more powerful than the strictness analyses by Jensen and Benton in that it in addition to strictness considers totality. So far we have only specified the analyses, however in order for the analyses to be practically useful we need an algorithm for inferring the annotated types. We construct an algorithm for the second analysis using the lazy type approach by Hankin and Le Métayer. The reason for choosing the second analysis from the thesis is that the approach is not applicable to the first analysis.</p><p>The third analysis we study is a binding time analysis. We take the analysis specified by Nielson and Nielson and we construct a more efficient algorithm than the one proposed by Nielson and Nielson. The algorithm collects constraints in a structural manner like the type inference algorithm by Damas. Afterwards the minimal solution to the set of constraints is found.</p><p>The last analysis in the thesis is specified by abstract interpretation. Hunt shows that projection based analyses are subsumed by PER (partial equivalence relation) based analyses using abstract interpretation. The PERs used by Hunt are strict, i.e. bottom is related to bottom. Here we lift this restriction by requiring the PERs to be uniform, in the sense that they treat all the integers equally. By allowing non-strict PERs we get three properties on the integers, corresponding to the three annotations used in the first and second analysis in the thesis.</p>

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